Question : In the figure given below, PQ is the diameter of the circle with centre O. If $\angle QOR=100^{\circ}$, then the measure of $\angle PSR$ is:
Option 1: $160^{\circ}$
Option 2: $80^{\circ}$
Option 3: $40^{\circ}$
Option 4: $100^{\circ}$
Correct Answer: $40^{\circ}$
Solution :
Given: $\angle POR = 100^\circ$
Now, POQ is a straight line.
⇒ $\angle POR + \angle QOR = 180^\circ$
⇒ $100^\circ+\angle POR = 180^\circ$
⇒ $\angle POR = 180^\circ- 100^\circ = 80^\circ$
Theorem:
The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
⇒ $\angle PSR = \frac{80^\circ}{2} = 40^\circ$
Hence, the correct answer is $40^\circ$.
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